Dielectric Relaxation in Dimethyl Sulfoxide/Water Mixtures Studied by MicrowaveDielectric Relaxation Spectroscopy

Zijie Lu,† Evangelos Manias,‡ Digby D. Macdonald,*,† and Michael Lanagan§

Center for Electrochemical Science and Technology, Polymer Nanostructures Laboratory, Department ofMaterials Science and Engineering, and Center for Dielectric Studies, Materials Research Laboratory, ThePennsylVania State UniVersity, UniVersity Park, PennsylVania 16802

ReceiVed: June 24, 2009; ReVised Manuscript ReceiVed: August 17, 2009

Dielectric spectra of dimethyl sulfoxide (DMSO)/water mixtures, over the entire concentration range, havebeen measured using the transmission line method at frequencies from 45 MHz to 26 GHz and at temperaturesof 298-318 K. The relaxation times of the mixtures show a maximum at an intermediate molar fraction ofDMSO. The specific structure of mixtures in different concentration regions was determined by the dielectricrelaxation dynamics, obtained from the effect of temperature on the relaxation time. A water structure “breakingeffect” is observed in dilute aqueous solutions. The average number of hydrogen bonds per water moleculein these mixtures is found to be reduced compared to pure water. The increase in the dielectric relaxationtime in DMSO/water mixtures is attributed to the spatial (steric) constraints of DMSO molecules on thehydrogen-bond network, rather than being due to hydrophobic hydration of the methyl groups. The interactionbetween water and DMSO by hydrogen bonding reaches a maximum at a DMSO molar fraction of 0.33,reflected by the maximum activation enthalpy for dielectric relaxation in this concentration, suggesting theformation of a stoichiometric compound, H2O-DMSO-H2O. In highly concentrated solutions, negativeactivation entropies are observed, indicating the presence of aggregates of DMSO molecules. A distinctantiparallel arrangement of dipoles is obtained for neat DMSO in the liquid state according to the Kirkwoodcorrelation factor (gK ) 0.5), calculated from the static permittivity. The similarity of the dielectric behaviorof pure DMSO and DMSO-rich mixtures suggests that dipole-dipole interactions contribute significantly tothe rotational relaxation process in these solutions.

1. Introduction

Water is a highly self-associated liquid with an open, lowcoordination number structure; the coordination number is about4.8 at 20 °C.1 A number of models have been proposed toaccount for the physical properties of water.2,3 Nevertheless,water remains an anomalous liquid where no single model isable to explain all of its properties.4 Ionic, polar, and hydro-phobic solutes perturb the structure of water in different wayswith profound consequences on their solubility, hydrationthermodynamics, and their association with other solutes. Solute-induced perturbations in the water structure are, in turn, lessunderstood than the structure of water itself and have long beena subject of controversy in chemistry, biology, and physiology.5

In this paper, we present and discuss results of a dielectricrelaxation study of aqueous solutions of dimethyl sulfoxide(DMSO). The interest in DMSO is due, in part, to the wide useof DMSO-H2O as solvents and reaction media. DMSO is apolyfunctional molecule with a highly polar SdO group andtwo hydrophobic CH3 groups. The partial negative charge onthe oxygen atom of DMSO molecule favors the formation ofthe hydrogen bonds with water molecules, whereas the nonpolarCH3 groups may give rise to hydrophobic hydration andhydrophobic association of DMSO molecules. Many observa-

tions6–8 suggest that DMSO forms hydrogen bonds with watermolecules throughout the whole composition range. Studies ofthe thermodynamic9,10 and transport properties11,12 of the DMSO/water system resulted in the generally accepted conclusion thatin the DMSO mole fraction range of 0.3-0.4 DMSO interac-tions with water, due to hydrogen bonding, are at a maximum.

The influence of DMSO on the molecular structure of liquidwater has been studied by many authors, and a number ofdifferent and often mutually exclusive explanations exist inliterature. The HH (water-H to water-H), MM (methyl-H tomethyl-H), and the MH (methyl-H to water-H) pair correlationfunctions in DMSO/water mixtures have been measured byLuzar and co-workers13–16 with neutron diffraction. The waterstructure is found to be weakly affected by the presence ofDMSO, but the percentage of water molecules that arehydrogen-bonded to each other is substantially reduced com-pared to pure water. Furthermore, no evidence for hydrophobicassociation of DMSO molecules has been observed in DMSO/water mixtures, which is similar to previous findings from IRspectroscopy of the OH and OD bands10,17 and other experi-ments.18 These results point to a “breaking” of water structurecaused by the presence of DMSO molecules. Many otherexperiments, including temperature of maximum density mea-surements19 and ionic conductance studies,20 also lead to theconclusion that small amounts of DMSO acts as a structurebreaker in water. On the other hand, neutron inelastic scatteringand X-ray diffraction studies7 and NMR measurements6,21

indicate that small amounts of DMSO increase the molecularorder of water. Infrared spectroscopy17 as well as density and

* Corresponding author. E-mail: ddm2@psu.edu. Tel.: (814) 863-7772.Fax: (814) 863-4718.

† Center for Electrochemical Science and Technology, Department ofMaterials Science and Engineering.

‡ Polymer Nanostructures Laboratory, Department of Materials Scienceand Engineering.

§ Center for Dielectric Studies.

J. Phys. Chem. A 2009, 113, 12207–12214 12207

10.1021/jp9059246 CCC: $40.75 2009 American Chemical SocietyPublished on Web 10/09/2009

partial molar volume measurements22 show that small quantitiesof DMSO have little effect on the water hydrogen bonding.Computer simulations of the structure of DMSO/water mixtureshave also been discussed on the basis of radial distributionfunctions.15,23–31 Typical molecular configurations, includingDMSO ·2H2O clusters, have been revealed in the simulations.DMSO was found to “enhance” the structure of water in verydilute solutions, whereas a further increase in DMSO concentra-tion in the solution led to a “breakdown” of the water structure.

Dielectric relaxation spectroscopy (DRS) probes the responseof the total dipole moment of a system, M(t) ) ∑µj(t), to atime-dependent external electrical field.32 This inherent abilityto monitor the cooperative motion of a molecular ensemblemakes it a powerful tool for investigating liquids whose structureand dynamics are dominated by intermolecular hydrogen bonds.Dielectric relaxation studies of DMSO/water mixtures have beenthe subject of several investigations.33–37 Kaatze et al.33 measuredthe dielectric spectra of the aqueous DMSO solutions in thewhole composition range at 25 °C between 1 MHz and 40 GHz.A strong increase of relaxation time with increasing DMSOconcentration was observed for the mixtures in the water-richregion. Similar behavior was also observed by Lyashchenko etal.34 and Puranik et al.36 This increase of relaxation time wasexplained to be due to the hydrophobic hydration effects simplyas an analogy with the increasing dielectric relaxation timesusually found around macromolecules. However, this analogyignores the effects of strong H-bonds between water and DMSOmolecules and may not be always correct. Buchner et al.38

applied the absolute reaction rate theory to determine thedielectric activation enthalpy and entropy for water from thedielectric relaxation times and to understand the moleculardynamics in water. The similar approach has been used in theinvestigation of alcohol/water systems.39 The same methodseems to be applicable to the DMSO/water mixtures. Therefore,a main purpose of this paper is to investigate the dielectricrelaxation in the DMSO/water mixtures in hope of understandingthe dielectric mechanism of the system.

It is also interesting to investigate dielectric relaxation of thehighly concentrated DMSO solutions. Dimethyl sulfoxide is aself-associated liquid, reflected by its high melting point (18.55°C), boiling point (189.0 °C), and high molar entropy ofvaporization (124 J ·K-1 ·mol-1). Infrared and Raman studies40–42

suggest the existence of dimers and higher polymers in liquidDMSO. A distinct antiparallel ordering of the molecular dipoleshas been observed by static permittivity measurements33 andby molecular dynamics simulation.23 In highly concentratedsolutions, insufficient water molecules are available to com-pletely hydrate the DMSO molecules. One would expect that itis solute-solute association that leads to the formation ofmicrophases in these solutions. But, one can also imagine thatmolecular complexes are formed by hydrogen bonding betweenDMSO and water molecules. For example, in DMSO-richmixtures, a recent molecular dynamics (MD) simulation29,30

revealed the existence of 1H2O-2DMSO cluster (an associationof a pair of DMSO molecules through their oxygen atoms linkedby one water molecule).

In view of the inconclusive results of previous studiesconcerning the structure of DMSO/water mixtures, it is ap-propriate to investigate the temperature dependence of thedielectric spectra of aqueous DMSO solutions over the wholecomposition range. Accordingly, in this study, we measured thedielectric relaxation spectra over a wide frequency range of 45MHz to 26 GHz and at temperatures ranging from 25 to 45 °C.The aim of this paper is to explore the relative contributions of

the hydrophobic and hydrophilic groups of DMSO to modifyingwater structure and to elucidate the structure of DMSO/watermixtures over the whole concentration range.

2. Experimental Section

Dimethyl sulfoxide (Sigma-Aldrich, 99.97%) was used asreceived. Double-distilled and deionized water (>18 MΩ,Millipore) was used in all the experiments. The DMSO/watermixtures at different DMSO mole fractions (xDMSO) wereprepared by mixing appropriate amounts of solute and solvent.

The complex permittivity spectra of the DMSO/water mix-tures in the frequency range from 45 MHz to 26 GHz weremeasured with a transmission line using a traveling-wavemethod. The wave transmitted through a liquid-filled coaxialline in the form of transmitted S-parameter (S21) was measuredby an HP8510C vector network analyzer. This technique waspreviously developed to measure the dielectric properties ofpolymer electrolyte membranes in the authors’ laboratory.43,44

In this work, the DMSO/water mixture sample was placed atthe end of a vertically positioned coaxial line of 7 mm o.d. and10 cm long. A thin layer of dielectric plug (vacuum grease inthis work), whose dielectric properties are close to that of air,was placed in the probe connector to prevent liquid leakage.The influence of the dielectric plug on the measurement hasbeen shown44 to be negligible and was not taken into accountin the solving for dielectric properties. Before measurement,the system was calibrated with an open, a short, and a knownload (50 Ω). Calibration of S21 magnitude was made byperforming a simple through connection with air as the dielectricmedium. Due to the high dielectric loss of the DMSO/watermixtures, several sample lengths, varying from 10 to 1 cm, wereused to obtain the optimal measurement of the dielectric spectra.Detailed explanation for the apparatus, the measurement pro-cedure, and the accuracy of the data as well as the validationof the technique for liquid media have been reported anddiscussed in ref 44.

DRS measurements were carried out at temperatures over therange of 25-45 °C at intervals of 5 °C. The coaxial line washeated by using a heating tape, and the temperature wascontrolled by a temperature controller to a precision of (0.5°C. The uncertainties of the complex permittivity values dependon the accuracy of the scattering parameters and on themagnitude of the ε′ and ε′′, themselves. Typical errors of lessthan 3% for ε′ and ε′′ were obtained.

The experimental dielectric spectra were fitted in a complexnonlinear least-squares routine by using various models repre-sented by the Havriliak-Negami function45

where εs is the static permittivity, ε∞ is the high-frequencylimiting permittivity, and τ is the relaxation time. R (0 e R e1) and (0e e 1) are shape parameters describing symmetricand asymmetric distribution of relaxation times, respectively.Three well-known models are limiting cases of this generalequation; they are the Debye equation (R ) 0, ) 1), theCole-Cole eq (0 e R < 1, ) 1), and the Davidson-Coleequation (R ) 0, 0 < e 1).

3. Results

Typical examples of the permittivity spectra of the DMSO/water mixtures in the whole composition range and at temper-

ε(ω) ) ε∞ +εs - ε∞

[1 + (jωτ)1-R](1)

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atures of 25-45 °C (298-318 K) are shown in Figures 1 and2, where Figure 1 shows the permittivity spectra of the mixturesover the entire concentration range at 298 K and Figure 2 showsthe spectra of the mixture of xDMSO ) 0.15 at 298, 308, and318 K. The plot in Figure 2b is commonly called a Cole-Coleplot. The dielectric spectrum of pure water in this frequencyrange is usually described as being a Debye relaxation.46–49 Therelaxation times and static permittivity obtained by fitting theexperimental data with a single Debye relaxation model are inaccordance with the literature data46–49 to within (0.5%. Thepermittivity spectra of pure DMSO are best fit by a Davidson-Cole function (R ) 0, 0 < e 1 in eq 1).33,50 The dielectricparameters of DMSO obtained in this work are in goodagreement with the literature data.33,50 The accurate measure-ments of the dielectric spectra of pure water and pure DMSOoffer further validation of the transmission line technique usedin this work.

The complex plane representation (i.e., Cole-Cole plot) ofthe dielectric spectra of the DMSO/water mixtures is a distortedcurve toward the real (ε′) axis (see Figure 2b), indicating thatthere is a distribution of relaxation times in these systems. Thepermittivity spectra, ε*(ω), of the mixtures at various composi-

tions were then analyzed by simultaneously fitting ε′(ω) andε′′(ω) to eq 1 with adjustable R and . The best results, i.e., theminimum variance of the fit and a consistent set of relaxationparameters as a function of composition and temperature, areobtained using the Davidson-Cole function (R ) 0 in eq 1).This is in agreement with the literature.33,36 In order to checkmore complicated spectral functions that might be related tomore specific solution models, as shown in the case of diethylsulfoxide/water mixtures,51 we also attempted to fit ε*(ω) by asum of multiple dispersion steps, where for each relaxationprocess a band shape defined by Debye, Cole-Cole, Davidson-Cole, or Havriliak-Negami function can be selected. However,for DMSO/water mixtures, even a sum of two simple Debyerelaxation processes, assuming a discrete contribution from waterand pure DMSO, has been proven to be invalid. This was alsopointed out by Kaatze et al.33 The authors are aware that theuse of Davidson-Cole spectral function is less theoreticallybased than the functions like Debye. However, recognizing aprevious fitting procedure described in the literature,33,36 webelieve that the Davidson-Cole function is the most appropriateway for displaying the frequency dispersion of the data.

Figure 1. Complex permittivity spectra (ε′ and ε′′) of DMSO/watermixtures at 25 °C at concentrations of (a) 0 e xDMSO e 0.33 and (b)0.4 e xDMSO e 1. The numbers in the figure represent the mole fractionof DMSO. The solid lines are the best fit with a Davidson-Colefunction.

Figure 2. (a) Complex permittivity spectra of a DMSO/water mixturewith the concentration of xDMSO ) 0.15 at 298, 308, and 318 K; (b)Cole-Cole diagram of ε′ and ε′′. Open symbols represent experimentaldata. The solid lines are calculated from the Davidson-Cole relaxationspectral function.

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The dielectric parameters obtained from the dielectric relax-ation spectra of mixtures through the Davidson-Cole functionare collected in Table 1 and also shown in Figures 3 and 4.From Figure 3, the spread of the relaxation time () sharplydecreases when small amounts of DMSO are added to water orwhen a small amount of water is added to DMSO. On furtheraddition of DMSO, a maximum value is obtained at xDMSO in

the range of 0.3-0.4. The change in values may reflect avariation in the relaxing species or a perturbation of themolecular structure of the system. The decrease of in the lowDMSO concentration region suggests that the structure of themixtures deviates significantly from that of pure water. Themaximum at xDMSO ) 0.3-0.4 may indicate the formation ofDMSO/2H2O complexes, for which xDMSO ) 0.33.

TABLE 1: Dielectric Parameters of the Davidson-Cole Relaxation Spectral Function (Eq 1 with r ≡ 0) for DMSO/WaterMixtures

εs (e (0.4) τ (ps) (e (0.3) (e (0.01) ε∞ (e (0.2) εs (e (0.4) τ (ps) (e (0.3) (e (0.01) ε∞ (e (0.2)

x ) 0 x ) 0.33298 K 78.89 8.25 1 5.2 298 K 68.97 52.78 0.86 3.97303 K 76.67 7.29 1 4.71 303 K 67.3 46.53 0.86 3.73308 K 74.65 6.48 1 4.21 308 K 65.62 39.25 0.859 3.51313 K 72.84 5.75 1 3.73 313 K 64.71 34.52 0.865 3.53318 K 70.64 5.17 1 3.25 318 K 63.8 30.31 0.87 3.56x ) 0.01 x ) 0.4298 K 78.11 9.37 0.97 4.65 298 K 66.98 53.94 0.865 4.55303 K 75.94 8.28 0.981 4.24 303 K 65.31 47.24 0.869 4.53308 K 73.78 7.14 0.991 3.83 308 K 63.63 40.12 0.867 4.51313 K 71.69 6.46 0.991 3.4 313 K 62.49 35.61 0.87 4.02318 K 69.6 5.98 0.99 2.96 318 K 61.34 31.26 0.87 3.52x ) 0.05 x ) 0.6298 K 78.02 14.65 0.882 4.26 298 K 59.83 42.88 0.815 5.0303 K 75.22 12.82 0.882 3.95 303 K 58.52 38.13 0.818 4.68308 K 72.43 11.44 0.884 3.65 308 K 57.21 34.66 0.82 4.35313 K 71.17 10.46 0.885 3.29 313 K 56.25 31.37 0.824 4.01318 K 69.92 9.50 0.886 2.94 318 K 55.30 28.88 0.822 3.66x ) 0.1 x ) 0.8298 K 76.79 22.53 0.816 4.27 298 K 53.51 30.95 0.798 3.8303 K 74.52 19.97 0.814 3.77 303 K 52.56 28.23 0.804 3.98308 K 72.24 17.94 0.811 3.28 308 K 51.62 25.48 0.809 4.14313 K 70.52 16.42 0.819 3.06 313 K 50.88 23.47 0.811 4.03318 K 68.8 14.97 0.827 2.84 318 K 50.13 22.08 0.813 3.9x ) 0.15 x ) 0.9298 K 75.16 31.98 0.81 3.91 298 K 50.40 25.93 0.822 4.24303 K 72.54 27.51 0.808 3.48 303 K 49.77 23.43 0.824 4.16308 K 69.93 24.53 0.805 3.05 308 K 49.13 21.65 0.823 4.07313 K 68.46 21.76 0.809 3.1 313 K 48.48 20.12 0.826 3.9318 K 66.98 19.18 0.813 3.15 318 K 47.83 18.86 0.827 3.72x ) 0.2 x ) 1298 K 74.64 40.13 0.845 3.74 298 K 47.29 20.92 0.895 4.45303 K 72.26 34.64 0.848 3.76 303 K 46.93 18.96 0.896 4.16308 K 69.88 29.87 0.847 3.78 308 K 46.64 17.81 0.896 3.86313 K 68.05 26.13 0.851 3.63 313 K 46.08 16.64 0.903 3.55318 K 66.23 23.48 0.854 3.49 318 K 45.53 15.63 0.91 3.23

Figure 3. Plot of relaxation time distribution parameter () of theDavidson-Cole function displayed as a function of mole fraction ofDMSO for DMSO/water mixtures over the temperatures of 298-318K at interval of 5 K.

Figure 4. Plot of relaxation time (τ) of the Davidson-Cole functiondisplayed as a function of mole fraction of DMSO for DMSO/watermixtures over the temperatures of 298-318 K at interval of 5 K.

12210 J. Phys. Chem. A, Vol. 113, No. 44, 2009 Lu et al.

The dielectric relaxation time, τ, as a function of thecomposition of the solution is shown in Figure 4. For eachtemperature, τ increases with xDMSO at small DMSO content,reaches a maximum when xDMSO is in the range of 0.3-0.4,and then decreases to the pure DMSO value. Previous studies33,34

have attributed the increase in the relaxation time with DMSOconcentration to hydrophobic hydration caused by the nonpolarmethyl groups, in an analogy with hydrophobic hydration inmacromolecules. However, this analogy ignores the effects ofthe strong hydrogen bonds between DMSO and water molecules.Therefore, the dielectric relaxation time information needsfurther analysis.

The dielectric relaxation can be treated as a rate processinvolving a path over a potential barrier.38,39,52,53 The energy ofactivation for the dielectric relaxation process, ∆G0,q, can becalculated from the dielectric relaxation time by using the Eyringequation

where T is the absolute temperature, and h, kB, and R are Plank’sconstant, Boltzmann’s constant, and the molar gas constant,respectively. A plot of ∆G0,q versus T (∆G0,q ) ∆H0,q - T∆S0,q)can yield the enthalpy ∆H0,q and entropy ∆S0,q of activationfor the dielectric relaxation process. These parameters character-ize the molecular interactions and dynamics of the componentsand their mixtures.

Figure 5 displays the free energy of activation as a functionof composition at temperature of 298, 308, and 318 K. Fromthis figure, we can see that ∆G0,q displays an extremely nonlineardependence on DMSO mole fraction between 298 and 318 K.These ∆G0,q versus xDMSO curves indicate that there exist stronginteractions between DMSO and water molecules, because, ifthe mixture was an ideal system, the free energy of activationof mixtures would have been represented by a straight linedetermined by ∆Gmix

0,q ) ∑i xi∆Gi0,q, (where x is the mole fraction

of the species and the subscripts mix and i represent the mixtureand pure components, respectively).

Figure 6 shows that ∆G0,q of DMSO/water mixtures is a linearfunction of temperature over the temperature range of 298-318K for all compositions. The values of ∆H0,q and ∆S0,q obtainedfrom this figure are displayed in Figure 7 as a function of

mixture composition. For most mixtures, |∆H0,q| > |T∆S0,q|,indicating that the reorientation processes in pure liquids andmixtures are controlled by enthalpic rather than by entropicfactors. Three different regions, separated by boundaries at xDMSO

∼0.1 and 0.6, are apparent from the dependencies of ∆H0,q and∆S0,q on composition, as shown in Figure 7. The followingsection will discuss the dielectric relaxation mechanism of themixtures in each region.

4. Discussion

4.A. Low-DMSO Region (0 e xDMSO e 0.1). The activationenthalpy (∆H0,q) and entropy (∆S0,q) for pure water arecalculated to be 15.9 kJ/mol and 20.7 J/mol ·K, respectively.These values are in good agreement with data in the literature.34,38

Buchner et al.38 related the ∆H0,q value to the H-bond probabilityin water. Assuming that only water molecules with one H-bondare mobile, they estimated the average number of hydrogenbonds per water, nHB, as

where ∆HHB is the strength of the hydrogen bond, ∼10.9 kJ/mol.54 Adding 1 in eq 3 is based on the fact that these “mobile”

Figure 5. Free energy of activation (∆G0,q) for the dielectric relaxationprocess in the DMSO/water mixtures as a function of the solutioncomposition at 298, 308, and 318 K.

∆G0,q ) RT ln(kBTτh ) (2)

Figure 6. Free energy of activation (∆G0,q) for the dielectric relaxationprocess in the DMSO/water mixtures as a function temperature. Thenumbers in the figure denote the mole fractions of DMSO.

Figure 7. Concentration dependence of the enthalpy (∆H0,q) and theentropy (∆S0,q) of activation plotted against the molar fraction ofDMSO.

nHB ) ∆H0,q

∆HHB+ 1 (3)

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molecules usually have one intact hydrogen bond. Thus, a valueof 2.5 is obtained for the average number of hydrogen bondsper water molecule in the liquid state at 298 K, which is closeto the literature value of 2.4,55 obtained with molecular dynamicssimulation, and of 2.8,56 obtained from density data.

When a small amount of DMSO (0 e x e 0.1) is added towater, ∆H0,q and ∆S0,q of the DMSO/water mixtures decreasefrom the values of pure water to a minimum at xDMSO ) 0.1(Figure 7). The decrease of ∆H0,q and ∆S0,q in the mixtures canbe attributed to two phenomena: a change in hydrogen-bondstrength or a decrease in the average number of hydrogen bonds.IR spectra measurements10 show that the addition of DMSOdid not change the distribution of hydrogen-bond energies ofwater. It is thus concluded that the reduction of ∆H0,q and ∆S0,q

is due to the decrease of average number of hydrogen bonds.Applying the similar method in eq 3 the average numbers ofH-bonds were also calculated for the dilute solutions, with theresults being summarized in Table 2. The reduction of nHB inthe mixtures means that the cooperative relaxation of thehydrogen-bond network is facilitated by the presence of DMSO.In other words, the DMSO molecules decrease the potentialbarrier for reorientation of the system dipole.

A hydrogen-bonding configuration has been proposed bySoper and Luzar13 to account for the neutron diffraction results.A similar configuration is redrawn in Figure 8, where a watermolecule is replaced by a DMSO molecule. Due to the abilityfor DMSO to accept two hydrogen bonds,23 the short-rangewater structure remains in the presence of DMSO molecules.Owing to the steric constraints of two methyl groups, whichprevent the further formation of hydrogen bonds on these sites,the total hydrogen bonds are decreased and the percentage ofwater molecules that are hydrogen-bonded to each other aresubstantially reduced compared to that in pure water (Figure8). This allows interpreting the reduced nHB values in themixtures obtained from the dielectric measurement. SinceDMSO forms stronger hydrogen bonds with water than waterdoes with itself,6–8,57 the hydrogen bonding between watermolecules is energetically more favorable to break or reformcompared to the H-bond between DMSO and water. Thus,dielectric relaxation in DMSO/water mixtures is essentially thesame process as it is in pure water, through the reorientation ofthe H-bonds between water molecules. The spatial stericconstraints imposed by DMSO molecules on the hydrogen-bondnetwork have at least two consequences: reducing the proportionof H-bonds that are energetically favorable and leading to longerwaiting time for destabilized hydrogen to rejoin the networkby forming new hydrogen bonds. Both of these two effects will

result in higher relaxation times. This accounts for the increasein relaxation times in mixtures.

This structure-breaking effect due to the strong hydrogenbonding between DMSO and water is clearly manifested alsoin the dielectric measurements. This result is consistent withmany other studies.10,19,23 Among them, the measurement of thetemperature of maximum density provides a direct indicationof water structure. Passage of the density through a maximumat 3.98 °C with increasing temperature is a unique property ofwater that can be attributed to a breakdown of the openhydrogen-bonded “flickering clusters” to form dense, nonstruc-tured water, superimposed upon the increase in molar volumeof both components as the temperature is raised. When a soluteis added to water to form an ideal solution (one that does nothave a specific impact on the structure of water) the temperatureof maximum density (Tm) changes by an amount that is readilycalculated from the properties of the system assuming idealbehavior. Subtraction of this change from the measured changein Tm yields a component that unequivocally reflects the impactof the solute on the unique structure of water. If the differenceis positive, the solute buttresses the structure of water and isdeemed to be a “structure maker”; if it is negative, the solute isa “structure breaker”. DMSO at low concentration is found tobe a water structure breaker.19 On the other hand, in a neutronand X-ray diffraction experiment, Stafford et al.7 observed anincrease in the RDF (radial distribution function) intensities indilute DMSO solutions and explained it as the promotion of

TABLE 2: Activation Parameters (∆H0,q, ∆S0,q) and theAverage Number of H-Bonds That Must Be Broken duringthe Relaxation Process in the Temperature Range of298-318 K

mole fraction ∆H0,q, kJ/mol ∆S0,q, J/mol ·K nHB

0 15.91 ( 0.15 20.67 ( 0.40 2.460.01 15.25 ( 0.45 17.45 ( 2.10 2.420.05 14.41 ( 0.40 10.92 ( 1.30 2.310.1 13.40 ( 0.45 3.95 ( 1.45 2.230.15 17.25 ( 0.45 13.94 ( 1.400.2 18.77 ( 0.55 17.18 ( 1.850.33 19.63 ( 0.55 17.66 ( 1.900.4 19.08 ( 0.50 15.70 ( 1.650.6 12.96 ( 0.40 -2.86 ( 1.200.8 10.98 ( 0.50 -6.83 ( 1.900.9 9.86 ( 0.50 -9.07 ( 1.601 8.67 ( 0.50 -11.26 ( 1.65

Figure 8. Schematic view of hydrogen bonding in pure water (a) andDMSO/water mixture (b). Solid lines represent intramolecular bonds;dashed lines represent hydrogen bonds.

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the water structure by the presence of DMSO molecules.However, this increase may reflect mostly concentration changesrather than the influence of the second component.23 Thecontribution from nonpolar methyl groups, if there is any, mayonly appear in extremely dilute solutions.

4.B. Region 0.15 < x < 0.4. As shown in Figure 7, the mostoutstanding feature for the dynamics of the mixtures in theconcentration region of 0.15 < x < 0.4 is that the activationenthalpy in this region is higher than that for pure water (Figure7). ∆H0,q reaches a maximum (20 kJ/mol) at x ) 0.33, whichis 1.3 times higher than that of pure water. This concentrationalso corresponds to the existence of minima or maxima inseveral thermodynamic properties.9–12 The explanation for thisphenomenon lies in the hydrogen-bonding configuration in themixtures. According to Figure 8, the fraction of H-bond formedbetween DMSO and water molecules increases as the DMSOconcentration increases, whereas the fraction of H-bond betweenwater molecules decreases. The ratio of these two types ofH-bonds will reach a maximum at a particular concentration.In view of the two hydrogen-bond accepting ability of theDMSO oxygen atom, the ratio will reach maximum at x ) 0.33,where the stoichiometric complex H2O-DMSO-H2O forms.At this concentration, each water molecule will be hydrogen-bonded to a DMSO molecule, and the mixture will behave likea homogeneous liquid, as reflected by the maximum in Figure3. The rotational relaxation of this mixture, without doubt,involves the hydrogen bond between DMSO and the watermolecule. The higher activation enthalpies in the second region,in comparison with the bulk water, are then due to the changeof the relaxation species, which have higher hydrogen-bondstrengths. The maximum relaxation time in this region couldbe a result of the stronger hydrogen bonding and longer lifetimeof these H-bonds.

The existence of stoichiometrically well-defined hydrogen-bonded DMSO/water aggregates is suggested here based on thearguments of ∆H0,q and ∆S0,q. Such aggregates are expected toadd distinct contributions to the dielectric spectrum. However,there is no evidence of a distinct contribution to the dielectricrelaxation in the spectra of these mixtures. This is not clearlyunderstood.33 The explanation may be that the radii of thedifferent aggregates in the system essentially have a continuousdistribution. However, an alternative interpretation may involvethe lifetimes of the different relaxation species. The relaxationtimes of aqueous DMSO solutions may reflect the productionrate of certain mobile species, including mobile water andDMSO molecules.

4.C. Pure DMSO and DMSO-Rich Region 0.6 < x e 1.In sharp contrast to the above two regions, negative entropiesof activation (∆S0,q) are obtained for the concentrated solutions,as seen in Figure 7. At the same time, the activation enthalpydecreases to less than the strength of a hydrogen bond (10.9kJ/mol). In the concentrated solutions, the complete hydrationof DMSO becomes impossible, because of the shortage of watermolecules. The interaction between DMSO molecules is thusbelieved to contribute significantly to the properties in thisregion.

In pure DMSO liquid, a distinct antiparallel ordering of themolecular dipoles has been observed by static permittivitymeasurements33 and by molecular dynamics simulation.23

The dipole correlation, expressed by the Kirkwood correlationfactor gK,58 for pure DMSO can be calculated according to theKirkwood-Frohlich equation32

where εs and ε∞ have the same meaning as above. N is thenumber of particles, V is the volume, and µ is the magnitude ofthe dipole moment. Taking the gas-state dipole moment, 3.91D,25 for µ, a value of 0.5 is obtained for gK of DMSO at 25 °Cfrom the permittivity data, indicating antiparallel ordering ofneighboring dipoles.33 The dipolar interaction energy betweenneighboring dipoles can be further calculated as a roughapproximation as

where r is the distance between two neighboring DMSOmolecules, which is approximately a molecular diameter. Witha molecular diameter of 5.6 A,25 one obtains E ) 6.4 kJ/molfrom eq 5. The activation enthalpy determined by the dielectricmeasurements is close to 9 kJ/mol (Table 2). Taking into accountthe oversimplification of the mean spherical molecule model,higher dipolar interaction energy is obtained in practice. It isthus concluded that antiparallel dipole-dipole interactionscontribute significantly to the formation of local order in liquidDMSO.

The clusters of DMSO would be expected to exist in highlyconcentrated solutions due to the same dipolar interactions. Intheory, the Kirkwood correlation parameter for the concentratedsolutions could be also determined through eq 4. However, theprecise determination of gK for the liquid mixtures is verydifficult owing to the complex interaction between the compo-nents. As a rough approximation, the average dipole momentis taken as µ ) (xwµw

2 + xDMSOµDMSO2)1/2. The value of gK for

the DMSO/water mixtures can thus be calculated from eq 4.Figure 9 shows the Kirkwood correlation factor gK for theDMSO-rich mixtures at 25, 35, and 45 °C. gK values of themixtures are smaller than 1, indicating the similar dipolecorrelation to that in pure DMSO. The significance of gK fordilute solutions is less important than in concentrated solutions,due to the prevailing hydrogen bonding in dilute solutions, andis not shown in this figure. Obviously, antiparallel ordering isalso significant in highly concentrated aqueous solutions.

5. Conclusions

The temperature dependence of the dielectric relaxationbehavior at microwave frequencies of DMSO/water mixtureswas investigated over the whole composition range. Thesemixtures exhibit different relaxation dynamics in differentconcentration regions, as revealed from an analysis of therelaxation time. At small DMSO mole fractions (xDMSO e 0.10),both the activation enthalpy and entropy decrease from the purewater values to minimum values at xDMSO ) 0.1. The averagenumber of hydrogen bonds per water molecule in the mixturesis calculated to decrease accordingly, assuming that the presenceof a small amount of DMSO does not significantly change thestrength of hydrogen bonding. A hydrogen-bonding configura-tion in DMSO/water mixtures is suggested, where a watermolecule in a hydrogen-bonding network is replaced by aDMSO molecule. Through this configuration, the breakdownof water structure is introduced. The increase in the relaxationtime in the mixtures does not appear to be due to thehydrophobic hydration of the methyl groups; instead it is due

εs - ε∞ )3εs

2εs + ε∞

4πN3kBTV

(ε∞ + 2)2µ2

9gK (4)

E )µ1µ2

4πε0r3

(5)

Dielectric Relaxation in DMSO/Water Mixtures J. Phys. Chem. A, Vol. 113, No. 44, 2009 12213

to the spatial steric constraints imposed by DMSO moleculeon the hydrogen-bond network. At intermediate DMSO molefractions (0.15 e xDMSO e 0.6), a stronger hydrogen bonding issuggested to form between DMSO and water molecules thanbetween water molecules, based on the higher activationenthalpies in these mixtures than in pure water. The activationenthalpy and entropy reach maximum at the DMSO molefraction of 0.33. It seems likely that hydrogen-bondedH2O-DMSO-H2O complexes are formed in the mixtures. Inthe DMSO-rich region (xDMSO g 0.6), the activation enthalpyis drastically decreased to less than the enthalpy of hydrogenbonding, and the activation entropy becomes negative. Thenegative activation entropy implies the self-association ofDMSO molecules in these mixtures, such that the rotationalactivated complex is a more ordered structure than is the initialstate. For neat DMSO liquid, an antiparallel arrangement ofdipoles is obtained from the Kirkwood correlation factor, gK )0.5. The dipolar forces also contribute significantly to thedielectric relaxation of DMSO-rich mixtures.

Acknowledgment. Z.L. acknowledges Mr. Steve Perini andMr. Khalid Rajab for help on dielectric measurements. Theauthors gratefully acknowledge financial support for this workby International Fuel Cells Inc. through subcontract no. 3540OBvia contract no. DE-FCo4-02AL67608 and by the U.S. Depart-ment of Energy via contract no. DE-FG02-07ER46371 at PennState University. E.M. additionally acknowledges support fromthe National Science Foundation (NSF Grant No. DMR-0602877).

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Figure 9. Kirkwood correlation factor (gK) as a function of molefraction of DMSO for the concentrated DMSO/water mixtures at 298,308, and 318 K.

12214 J. Phys. Chem. A, Vol. 113, No. 44, 2009 Lu et al.